stats exam 3
what is a parameter
a numerical description of a population
True or false? If the sample mean of a random sample from an x distribution is relatively small, when the confidence level c is reduced, the confidence interval for μ becomes shorter.
True. As the level of confidence decreases, the maximal error of estimate decreases.
what is a statistic
a numerical description of a sample
as the confidence level (C) increases
the margin of error (E) increases
as the standard deviation increases
the margin of error (E) increases
as the standard deviation decreases
the margin of error decreases
as sample size decreases
the margin of error increases
what is a sampling distribution
the probability distribution of a sample statistic
Sam computed a 95% confidence interval for μ from a specific random sample. His confidence interval was 10.1 < μ < 12.2. He claims that the probability that μ is in this interval is 0.95. What is wrong with his claim?
Either μ is in the interval or it is not. Therefore, the probability that μ is in this interval is 0 or 1.
True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for μ.
False. Different random samples may produce different values, resulting in different confidence intervals.
as sample size increases
margin of error decreases
List these from smallest margin of error to largest margin of error a) A 99% confidence interval with a sample size of 50. b) A 99% confidence interval with a sample size of 25. c) A 90 % confidence interval with a sample size of 50. d) A 95% confidence interval with a sample size of 50.
C, D, A, B
True or false? If the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for μ will be relatively short.
False. The maximal error of estimate controls the length of the confidence interval regardless of the value of .
True or false? A larger sample size produces a longer confidence interval for μ.
False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.
statistic standard deviation
S
True or false? If the original x distribution has a relatively small standard deviation, the confidence interval for μ will be relatively short.
True. As σ decreases, E decreases, resulting in a shorter confidence interval.
true or false The value zc is a value from the standard normal distribution such that P(-zc < z < zc) = c.
True. By definition, critical values zc are such that 100c% of the area under the standard normal curve falls between -zc and zc.
True or false? Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating μ is the magnitude of the difference between and μ.
True. By definition, the margin of error is the magnitude of the difference between and μ.
True or false? The point estimate for the population mean μ of an distribution is x, computed from a random sample of the x distribution.
True. The mean of the distribution equals the mean of the x distribution and the standard error of the distribution decreases as n increases.
Sam computed a 90% confidence interval for μ from a specific random sample of size n. He claims that at the 90% confidence level, his confidence interval contains μ. Is this claim correct? Explain.
Yes. The proportion of all confidence intervals based on random samples of size n that contain μ is 0.90.